Question

Solve for x/x5=20(1 point)

Answer 1

To solve the equation \( \frac{x}{x^5} = 20 \), we can simplify the left side.

First, note that \( \frac{x}{x^5} = \frac{1}{x^4} \). So we can rewrite the equation as:

\[
\frac{1}{x^4} = 20
\]

Now, take the reciprocal of both sides to eliminate the fraction:

\[
x^4 = \frac{1}{20}
\]

Next, we take the fourth root of both sides to solve for \( x \):

\[
x = \left(\frac{1}{20}\right)^{\frac{1}{4}} = \frac{1^{\frac{1}{4}}}{20^{\frac{1}{4}}} = \frac{1}{20^{\frac{1}{4}}}
\]

We can simplify \( 20^{\frac{1}{4}} \):

\[
20^{\frac{1}{4}} = (2^2 \cdot 5)^{\frac{1}{4}} = 2^{\frac{1}{2}} \cdot 5^{\frac{1}{4}} = \sqrt{2} \cdot 5^{\frac{1}{4}}
\]

Thus, the answer for \( x \) is:

\[
x = \frac{1}{\sqrt{2} \cdot 5^{\frac{1}{4}}}
\]

This represents the value of \( x \) that satisfies the original equation. If you're looking for a decimal approximation, you can compute that value as needed.

Alternatively, if you just want the most straightforward form based on \( 20 \):

\[
x = 20^{-\frac{1}{4}}
\]

Thus, the solution is:

\[
x = 20^{-\frac{1}{4}} \quad \text{or} \quad x = \frac{1}{\sqrt{2} \cdot 5^{\frac{1}{4}}}
\]